# Reasoning Is Not Free: Robust Adaptive Cost-Efficient Routing for LLM-as-a-Judge

arXiv: https://arxiv.org/abs/2605.10805 · HTML: https://mlsanity.com/paper/2605.10805/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 34 of its 65 references that are in the map.
- First posted on arXiv 11 May 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 34)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [M3-Embedding: Multi-Linguality, Multi-Functionality, Multi-Granularity Text Embeddings Through Self-Knowledge Distillation](https://mlsanity.com/paper/2402.03216/) (2024)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [Kimi K2: Open Agentic Intelligence](https://mlsanity.com/paper/2507.20534/) (2025)
- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [Skywork-Reward: Bag of Tricks for Reward Modeling in LLMs](https://mlsanity.com/paper/2410.18451/) (2024)
- [JudgeBench: A Benchmark for Evaluating LLM-based Judges](https://mlsanity.com/paper/2410.12784/) (2024)
- [Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs](https://mlsanity.com/paper/2406.18629/) (2024)
- [RouterBench: A Benchmark for Multi-LLM Routing System](https://mlsanity.com/paper/2403.12031/) (2024)
- [RM-Bench: Benchmarking Reward Models of Language Models with Subtlety and Style](https://mlsanity.com/paper/2410.16184/) (2024)
- [Llama-Nemotron: Efficient Reasoning Models](https://mlsanity.com/paper/2505.00949/) (2025)
- [RM-R1: Reward Modeling as Reasoning](https://mlsanity.com/paper/2505.02387/) (2025)
- [RewardBench 2: Advancing Reward Model Evaluation](https://mlsanity.com/paper/2506.01937/) (2025)
- [Olmo 3](https://mlsanity.com/paper/2512.13961/) (2025)
- [AutoMix: Automatically Mixing Language Models](https://mlsanity.com/paper/2310.12963/) (2023)
- [Personalization of Large Language Models: A Survey](https://mlsanity.com/paper/2411.00027/) (2024)
- [Learning to Plan & Reason for Evaluation with Thinking-LLM-as-a-Judge](https://mlsanity.com/paper/2501.18099/) (2025)
- [JudgeLRM: Large Reasoning Models as a Judge](https://mlsanity.com/paper/2504.00050/) (2025)
- [Distributionally Robust Optimization: A Review](https://mlsanity.com/paper/1908.05659/) (2019)
- [J1: Incentivizing Thinking in LLM-as-a-Judge via Reinforcement Learning](https://mlsanity.com/paper/2505.10320/) (2025)
- [ThinkSwitcher: When to Think Hard, When to Think Fast](https://mlsanity.com/paper/2505.14183/) (2025)
- [Prompt-to-Leaderboard](https://mlsanity.com/paper/2502.14855/) (2025)

## Built on by (most cited first, 2 of 2)

- [CodeRescue: Budget-Calibrated Recovery Routing for Coding Agents](https://mlsanity.com/paper/2607.19338/) (2026)
- [RAIM: Robust Aggregation of Inexpensive Models for Hallucination Detection](https://mlsanity.com/paper/2609.39229/) (2026)

## Abstract (arXiv)

Reasoning-capable large language models (LLMs) have recently been adopted as automated judges, but their benefits and costs in LLM-as-a-Judge settings remain unclear. Through controlled comparisons between reasoning and non-reasoning judges, we show that explicit reasoning substantially improves judgment accuracy on tasks requiring structured verification (e.g., math and coding), while offering limited or even negative gains on simpler evaluations and incurring significantly higher computational cost. These findings motivate that reasoning should be used selectively rather than universally, with awareness of possible distribution shift. We propose a Robust Adaptive Cost-Efficient Routing (RACER), which dynamically selects between reasoning and non-reasoning judges under a fixed budget by formulating routing as a constrained distributionally robust optimization problem. RACER explicitly accounts for distribution shift via a KL-divergence uncertainty set, admits an efficient primal--dual algorithm, and enjoys theoretical guarantees including uniqueness of the optimal policy and linear convergence. Extensive experiments show that RACER achieves superior accuracy--cost trade-offs under distribution shift.